I am being biased here, but I’d recommend having a look at Brand24. Here are a couple of tips for starters:
-add your competitors’ names as monitored keywords
-monitor their domains as some people tend to include the domains rather than social media handles in their
posts
-monitoring branded hashtags is worth considering, too.
Sentiment filter is a super valuable feature that allows for filtering the mentions according to people’s attitude expressed in their posts. With that being said, you can easily get to those mentions from people dissatisfied with your competitors’ services or products.
Quite often I see people looking for help or asking questions on social media that some brands do not bother to reply to. If you're capable of helping those people, there’s nothing wrong in jumping in such conversations. Someone else’s negligence might actually turn out a win for you.
You might also want to check https://similarweb.com and https://semrush.com out. The former enables me to compare the number of visits against competitors as well as average visit duration, pages per visit, or bounce rate. The comparison of traffic sources is also worth having a detailed look into. The latter is extremely helpful while doing a keywords analysis and finding both organic and paid keywords your competitors are using.

A great tool that helps me understand where and how people discuss certain topics like "Alternative to [MyCompetitorName]", "How to [Solve the problem I sell a solution to]" so I can engage personally and try to convert.

Brand24 is a great app, especially if you're a business prone to any type of social media critics (like every type of business, nowadays?). It's just a much better way to know what people are saying about your brand then searching it through Google.

Since Google crawls practically all things, you can piggy-back on what it finds based on any string combination you want using @GoogleAlerts.
Then you can setup these alerts to flow into a separate email account that's setup with filters based on new alert content.
So, lets say you want alerts on "Blockchain" that Google finds, just setup that alert and then your email will populate with references to "Blockchain" that occur across the web.

Just suggested the same for SEO - If you're looking for a paid one and inclined towards knowing more about competition, then Ahrefs. It's data-driven (much more than SEO) -they crawl 6 billion pages every day and you can learn almost everything about your competitors. It helps to know where your competition is getting traffic from, exact keywords they use, how much traffic it brings them and how many backlinks & who exactly links to their website. You can also set “Alerts” for website rankings or mentions.

No other tool reports most of the new mentions for a brand.
Google Alerts is broken for years and the other tools report fragmented sets of data.
The aim of the tool is to report as many relevant web mentions as possible.
It also filters spammy and irrelevant mentions.
You can setup email alerts to notify you daily or weekly when new mentions appear.

Personal brands, small businesses and even enterprise level clients can all benefit greatly from using BrandMentions. Real-time monitoring and responding is becoming more and more important with such a fast pace online world we live in today. Having tried and tested relevant competitors to BrandMentions I can honestly say that the quality of data BrandMentions provide is better.

I have been using Brand Mentions for about 3 months now, and it has become an asset to my company. Having the ability to track any mention of my company allows me to see any feedback, and also helps with our product roadmap. I am a huge fan, and would recommend Brand Mentions to everyone!

Subscribe to relevant news sources, product update feeds, competitor press release pages, track keywords across the RSS space, and more. Also useful for keeping a tab on analog products and markets. You can curate your findings into collections collaboratively with your team and publish.